73,252 research outputs found
Permutation and Grouping Methods for Sharpening Gaussian Process Approximations
Vecchia's approximate likelihood for Gaussian process parameters depends on
how the observations are ordered, which can be viewed as a deficiency because
the exact likelihood is permutation-invariant. This article takes the
alternative standpoint that the ordering of the observations can be tuned to
sharpen the approximations. Advantageously chosen orderings can drastically
improve the approximations, and in fact, completely random orderings often
produce far more accurate approximations than default coordinate-based
orderings do. In addition to the permutation results, automatic methods for
grouping calculations of components of the approximation are introduced, having
the result of simultaneously improving the quality of the approximation and
reducing its computational burden. In common settings, reordering combined with
grouping reduces Kullback-Leibler divergence from the target model by a factor
of 80 and computation time by a factor of 2 compared to ungrouped
approximations with default ordering. The claims are supported by theory and
numerical results with comparisons to other approximations, including tapered
covariances and stochastic partial differential equation approximations.
Computational details are provided, including efficiently finding the orderings
and ordered nearest neighbors, and profiling out linear mean parameters and
using the approximations for prediction and conditional simulation. An
application to space-time satellite data is presented
Fast modal extraction in NASTRAN via the FEER computer program
A new eigensolution routine, FEER (Fast Eigensolution Extraction Routine), used in conjunction with NASTRAN at Israel Aircraft Industries is described. The FEER program is based on an automatic matrix reduction scheme whereby the lower modes of structures with many degrees of freedom can be accurately extracted from a tridiagonal eigenvalue problem whose size is of the same order of magnitude as the number of required modes. The process is effected without arbitrary lumping of masses at selected node points or selection of nodes to be retained in the analysis set. The results of computational efficiency studies are presented, showing major arithmetic operation counts and actual computer run times of FEER as compared to other methods of eigenvalue extraction, including those available in the NASTRAN READ module. It is concluded that the tridiagonal reduction method used in FEER would serve as a valuable addition to NASTRAN for highly increased efficiency in obtaining structural vibration modes
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